[mothered]

They took no signature and they have a picture of the package in the driver's hand in front of my house.

It doesn't hold any grounds that the package was "received" by the account holder. The driver having possession of the package and It being accepted by the recipient, are two different things altogether.

A signature was not taken, nor Is there any evidence to solidify that It was received by you.
Based on this, try the didn't arrive method.

Should I try to say that the person he gave it to was not [My Mother's Name]? if he does show up? Thanks.

Judging by the following, they have no evidence suggesting the Item was received by anyone In your household.

They took no signature and they have a picture of the package in the driver's hand in front of my house.

The driver Is standing In front of your house. So what? So too are uninvited guests- both do not Indicate you've played any part In accepting their arrival. As far as you're concerned, the package didn't arrive.